A pseudo-hilbert scan for arbitrarily-sized arrays

The 2-dimensional (2-D) Hilbert curve is a one-to-one mapping between 2-D space and one-dimensional (1-D) space. It is studied actively in the area of digital image processing as a scan technique (Hilbert scan) because of its property of preserving the spacial relationship of the 2-D patterns. Currently there exist several Hilbert scan algorithms. However, these algorithms have two strict restrictions in implementation. First, recursive functions are used to generate a Hilbert curve, which makes the algorithms complex and computationally expensive. Second, both sides of the scanned rectangle must have same size and each size must be a power of two, which limits the application of the Hilbert scan greatly. In this paper, a Pseudo-Hilbert scan algorithm based on two look-up tables is proposed. The proposed method improves the Hilbert scan to be suitable for real-time processing and general application. The simulation indicates that the Pseudo-Hilbert scan can preserve point neighborhoods as much as possible and take advantage of the high correlation between neighboring lattice points. It also shows competitive performance of the Pseudo-Hilbert scan in comparison with other scan techniques.